Question

A fruit seller buys some apples at the rate of 5 for Rupees 6 and an equal number more at 4 for Rupees 5. He sells the whole lot at 9 for Rupees 11. What is his loss or gain percent?

• A. loss $\dfrac{100}{441}$ %
• B. gain $\dfrac{100}{441}$ %
• C. No profit No loss
• D. Loss $\dfrac{5}{22}$ %

Hint:

When equal numbers of items are bought at different rates, take the LCM of quantities to simplify calculations. Always compute total C.P. and S.P. carefully before calculating percentage profit or loss.

Answer 1

The Correct Option is A

Step 1: Take a convenient total, say 180 apples in each lot (a multiple of 5, 4, and 9). Cost of 180 apples at 5 for Rupees 6 is \(\dfrac{180}{5}\times6=216\); cost of 180 apples at 4 for Rupees 5 is \(\dfrac{180}{4}\times5=225\). Total cost \(=216+225=441\) for 360 apples.

Step 2: Selling price of all 360 apples at 9 for Rupees 11 is \(\dfrac{360}{9}\times11=440\).

Step 3: Since selling price (440) is less than cost price (441), there is a loss of \(441-440=1\). Loss percent \(=\dfrac{1}{441}\times100=\dfrac{100}{441}\%\). \[ \boxed{\text{Loss } \dfrac{100}{441}\%} \]